Unicellular operators

Barría, José; Davidson, Kenneth R.

doi:10.1090/S0002-9947-1984-0742423-2

Unicellular operators
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by José Barría and Kenneth R. Davidson

Trans. Amer. Math. Soc. 284 (1984), 229-246

DOI: https://doi.org/10.1090/S0002-9947-1984-0742423-2

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Abstract:

An operator is unicellular if its lattice of invariant subspaces is totally ordered by inclusion. The list of nests which are known to be the set of invariant subspaces of a unicellular operator is surprisingly short. We construct unicellular operators on ${l^p},1 \leqslant p < \infty$, and on ${c_0}$ with lattices isomorphic to $\alpha + X + {\beta ^{\ast }}$ where $\alpha$ and $\beta$ are countable (finite or zero) ordinals, and $X$ is in this short list. Certain other nests are attained as well.

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